where SYS_NC00062$ is not a column directly specified in the sql but a virtual column related to a function-based index.

This matches a bug which is currently under development and not yet published (Bug 7026584).

The explanation is that the 11g optimizer uses a new mechanism to work with function-based indexes at parse time, a new mechanism which as yet not fully robust.

The problem comes when virtual column processing is done from qkacol where it clones the predicates and later tries to resolve the copied columns in the predicate with the supplied fro. The root cause here, the unnesting driver generates an alias for table and adds it for a correlated column. [sic]

In addition to the 10046 and 10053 trace files, a 904 errorstack trace file provided the information required:

alter system set events='904 trace name errorstack';
...
alter system set events='904 trace name errorstack off';

Oracle’s currently (at the time of writing this) recommended solution to that bug to set undocumeted parameter _replace_virtual_columns to false.